Soit k un corps de caractéristique ≠2 dans lequel −1 est un carré, et soit A une algèbre simple centrale sur k de degré 4. La forme trace de A s'écrit de façon unique comme une somme (au sens de Witt)
Let k be a field of characteristic different from 2 containing a primitive 4-th root of unity. We show that the trace quadratic form of any central simple k-algebra A of degree 4 decomposes in the Witt group of k as the sum of a 2-fold Pfister form
Accepté le :
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Markus Rost 1 ; Jean-Pierre Serre 2 ; Jean-Pierre Tignol 3
@article{CRMATH_2006__342_2_83_0, author = {Markus Rost and Jean-Pierre Serre and Jean-Pierre Tignol}, title = {La forme trace d'une alg\`ebre simple centrale de degr\'e 4}, journal = {Comptes Rendus. Math\'ematique}, pages = {83--87}, publisher = {Elsevier}, volume = {342}, number = {2}, year = {2006}, doi = {10.1016/j.crma.2005.11.002}, language = {fr}, }
Markus Rost; Jean-Pierre Serre; Jean-Pierre Tignol. La forme trace d'une algèbre simple centrale de degré 4. Comptes Rendus. Mathématique, Volume 342 (2006) no. 2, pp. 83-87. doi : 10.1016/j.crma.2005.11.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.11.002/
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